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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 3202. |
Making use of the method of replacing an infinitesimal with an equivalent one, find the following limits: underset(x to 0)lim (sin 3x)/(ln (1+5x)) (b) underset(x to 0)lim (ln (1+sin 4x))/(e^(sin 5x)-1) (c ) underset(x to 0) (e^(sin 3x)-1)/(ln (1+tan 2x)) (d) underset(x to 0)lim (arc tan 3x)/(arc sin 2x) (e ) underset(x to 0)lim (ln (2-cos 2x))/(ln^(2) (sin 3x+1)) (f) underset(x to 0)lim (sqrt(1+sin 3x)-1)/(ln (1+tan 2x)) (g) underset(x to 0)lim ln (1+2x-3x^(2)+4x^(3))/(ln (1-x+2x^(2)-7x^(3)) (h) underset(x to 0)lim (sqrt(1+x^(2))-1)/(1-cos x) |
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| 3204. |
(Manufacturing problem): A manufacturer has three machines. I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the sue of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machies are given in the follownig table: She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each item should be produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit? |
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| 3205. |
Relation " parallel" in the straight line in a plane is : |
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Answer» only reflexive |
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| 3206. |
x in R the least value of (x^(2)-6x+5)/(x^(2)+2x+1) |
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Answer» -1 |
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| 3207. |
int (x^(5//2))/(sqrt(1 + x^(7)))dx = |
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Answer» `(2)/(7) LOG (x^(7//2) + SQRT(x^(7) + 1)) + C ` |
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| 3208. |
The original price of a shirt is x dollars. During a sale , the original price is marked down y percent. On the last day of the sale , an additional discount of z percent off the sale price is offered. Which of the following represents the price of the shirt , in dollars , after the additional discount ? |
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Answer» `(XYZ)/((100)(100))` |
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| 3209. |
iftheinequationsqrt(x+5 lt-xthen |
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Answer» 5ltxlarr1 |
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| 3210. |
A house wife wishes to mix together two kinds of foot F_(1) and F_(2) in such a way that the mixturecontains at least 10 units of vitamin A, 12 units of vitamin Band 8 units of vitamin C. Thevitamins contained in one kg of foods F_(1) and F_(2) are as below . {:(,"Vitamin A "," Vitamin B "," Vitamin C " ),("Food " F_(1),""1,""2,""3),("Food " F_(2) ,""2,""2,""1):} Formulate as an L.P.P. and find least cost of the mixture which will produce the dietif 1 kg of food F_(1) costs ₹ 6 and one kg of food F_(2)cost ₹ 10 |
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| 3211. |
Prove that the function f defined by f(x) ={{:((x)/(|x|+2x^(2)), if x ne 0),(k,if x = 0):}remainsdiscontinuous at x= 0,regardingsthe choice iof k. |
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Answer» At `x= 0, LHL =underset(xrarr0^(-))(lim)(x)/(|x|+2x^(2)) = underset(hrarr0)(lim)((0-h))/(|0-h|+2(0-h)^(2))` `= underset(hrarr0)(lim)(-h)/(h+2h^(2))=underset(hrarr0)(lim)(-h)/(h(1+2h)) = -1` `RHL= underset(xrarr0^(+))lim(x)/(|x|+2x^(2))= underset(hrarr0)(lim)(0+h)/(|0+h|+2(0+h)^(2))` `= underset(hrarr0)(lim)(h)/(h+2h)^(2)=underset(hrarr0)(lim)(h)/(h(1+2h)) = 1` and`f(0) =k` Since, ` LHL neRHL` for anyvalue of k. Hence, `f(x)` is discountinuousat `x = 0`regardiess the choiceofk. |
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| 3212. |
On Z, the set of integers, define a relation R on Z as follows: aRb if ab ge 0, Then |
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Answer» R is reflexive and symmetric only |
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| 3214. |
Integrate the function is Exercise. (1)/((x^(2)+1)(x^(2)+4)) |
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| 3215. |
ABC is a triangle where a=6, b=3 and cos(A-B)=4/5 |
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Answer» `1/(2sqrt(5))` |
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| 3216. |
Let p, q and r be three logical statements. Which of the following-is true? |
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Answer» ~ `(p VV ~ q ) equiv ~ p vv q` |
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| 3217. |
How many of the following liberate O_(2) on heating in a dry test tube ? CaO, Fe_(2)O_(3), Fe_(3)O_(4), FeO, Cr_(2)O_(3), XeF_(4), Al_(2)O_(3), MgO, Na_(2)O |
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| 3218. |
The solutions of (x+d+1)dy=dx are- |
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Answer» `x+y+2=ce^(y)` |
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| 3219. |
If AB=AandBA=Bthen A^(2)+B^(2)= ……….. |
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Answer» `A+B` |
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| 3220. |
The value of the expression ( 1 + (1)/(omega)) ( 1 + (1)/(omega^(2)))+ (2+ (1)/(omega)) (2 + (1)/(omega^(2))) + (3 + (1)/(omega)) (3 + (1)/(omega^(2))) + …… + ((n + (1))/(omega)) (n + (1)/(omega^(2))) Where omega is an imaginary cube root of unity, is |
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Answer» `(N(n^(2) + 2))/(3)` |
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| 3221. |
Three vectors 7hati-11hatj+hatk, 5hati+3hatj-2hatk and 12hati-8hatj-hatk forms |
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Answer» an EQUILATERAL triangle `=7(-3-16)+11(-5+24)+1(-40-36)` `=-133+209-76=0` So, the vectors are collinear |
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| 3222. |
The rate of change of radius of a circle is 1 cm / sec. Match the following |
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Answer» d,b,c,a |
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| 3223. |
Integrate the following functions : int(a^(x)+a^(-x))^(3)dx |
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| 3224. |
An item is manufactured by three machines A, B and C. Out of the total number of items manufactured during a specified period, 50% are manufactured on A, 30% on B and 20% on C. 2% of the items produced on A and 2% of items produced on B are defective, and 3% of these produced on C are defective. All the items are stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine A ? |
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| 3225. |
If vecx and vecy are two unit vectors and pi is the angle between them then 1/2|vecc -vecy| is equal to |
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| 3226. |
Assertion (A) : int (2 x tan x sec^(2) x + tan^(2) x) dx = x tan^(2) x + c Reason (R) : int (x f^(1) (x) +int(x) ) dx = x f(x) + c The correct answer is |
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Answer» Both (A) and (R) are true and (R) is the correct EXPLANATION of (A) |
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| 3227. |
A block starting from rest slides down a rough fixed incline having anlge of inclination 53^(@).It covers 12m in first two seconds i.e from t=0 to t=2 sec then : |
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Answer» VELOCITY at t= 2 SEC will be 12 `m//s` |
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| 3228. |
Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p,N x 3 and Respectively.If n =p , then the order of the matrix 7X-5Z is : (A) pxx2 (B) 2xxn (C ) nxx3 (D) pxxn |
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| 3229. |
Find the domains of definaton of the following functions: (a) f(x)=sqrt(arc sin (log_2x)), (b) f(x)=log_(2) log_(3) log _(4) x, (c) f(x)=1/x +2^(arc sinx)+1/sqrt(x-2) (d) f(x)=log|4-x^(2)|, (e) f(x)=sqrt(cos(sin x)+arc sin ""(1+x^(2))/(2x) Find the ranges of the following functions: (f) y=1/(2-cos 3x) (g) y=x/(1+x^2) |
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| 3230. |
Compute P for n=8,r=4 |
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Answer» Solution :`n=8,r=4` `:.""^nP_r=(n!)/((n-r)!)=(8!)/((8-4)!)` `=(8*7*6*5*4*!)/(4!)=8*7*6*5=1680` |
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| 3231. |
Select the correct answer:Order of (d^2y/(dx^2))^3+sin(dy/dx)+x=0 |
| Answer» Answer :C | |
| 3232. |
Show that sqrt2 is irrational. |
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| 3233. |
Three coins are tossed together. If X denotes the numbers of heads obtain on it. Then obtain mean, variance and standard deviation of distribution. |
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| 3234. |
Show that : Lt_(x to a)(sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x))=(2)/(3 sqrt(3)) |
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| 3235. |
A guardof12 menis formeda group of nsoldiers. Itis foundthat2 particularsoldersA and B are3 timesas often togetheronguardas3particularsoldersC,D,& E.Then n= |
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Answer» 31 |
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| 3236. |
Solve the system: x sin a + y sin 2a + z sin 3a = sin 4a x sin b + y sin 2b + z sin 3b = sin 4b x sin c + y sin 2c + z sin 3c = sin 4c |
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Answer» y = - 2 - 4(cos a cos b + cos c + cos b cos c) Z = 2(cos a + cos b + cos c) |
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| 3237. |
Statement-I: int (dx)/(sqrt(9 -x^(2))) = sin^(-1) ((x)/(3)) + c Statement -II: int (" cos x dx ")/(sqrt(16 - sin^(2) x)) = sin^(-1)((sin x)/(4)) + c Which of the following s true ? |
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Answer» Only I |
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| 3238. |
If the roots of x^(2)-bx+c=0 are two consecutive integers, then b^(2)-4c is |
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Answer» 0 |
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| 3239. |
For the post of principal in school three persons A, B and C are candidates. Probability of their appointment is in ratio 4 : 2 : 3. If school time will changes to morning then probability of the appointment of candidate will be 0.3, 0.5 and 0.8 respectively. Then find probability of an event that school time changes to morning. |
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Answer» `(21)/(45)` |
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| 3240. |
A : Ifsin x + " cosec "x=2 , " then " sin^(n)x+"cosec"^(n)x=2 R : If x gt 0 , " then " x + (1)/(x) ge 2 |
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Answer» A is true , R is true and R is CORRECT explanation of A |
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| 3242. |
Evaluate :int((x^3+8)(x-1))/(x^2-2x+4)dx |
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| 3243. |
If P(n )is thestatement, ' ' (1)/( 1xx 2) + (1)/( 2xx 3) +(1)/( 2 xx 3)+(1)/( 3 xx4)+ ….. + (1)/(n(n +1))= (n)/(n +1)'thenP(n)is truefor |
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Answer» `NGT 2` |
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| 3244. |
The sum of the series (12)/(2!)+(28)/(3!)+ (50)/(4!) + ( 78)/(5!)+"......." is |
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Answer» EQUAL |
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| 3245. |
Match the following: |
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Answer» `{:(P,Q,R,S),(2,1,4,3):}` |
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| 3246. |
Direction ratios of a line L_(1), ae 1,-1,1 and of L_(2) re 1,0,lambda. Find the value of lambda so that L_(1)andL_(2) are perpendicular to each other. |
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| 3247. |
For three events A,B and CP (exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C ir A occurs) = P and P(all the three events occur simultaneously) =P^(2), where 0ltplt(1)/(2) Then the probability of at least one of the three events A,B and C occuring is : |
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Answer» `(3p+2p^(2))/(2)` SIMILARLY for B or C , C or A Adding all THREE, we get, `P(A)+P(B)+P(C )-P(A nn B)-P(B nn C)-P(C nn A)=(3p)/(2)` `P(A uu B uu C)=(3p)/(2)+p^(2)` |
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| 3248. |
Match the following: |
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Answer» <P>`{:(P,Q,R,S),(2,1,4,3):}` |
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| 3249. |
Integrate the following functions sqrt(tanx)/(sinx cosx) |
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Answer» Solution :`sqrt(TANX)/(sinx cosx) = sqrt(tanx)/(cos^2x (sinx/cosx))` =`sqrt(tanx)/(cos^2x tanx) = sec^2x/sqrt(tanx)` = Let t = tanx. Then dt = `sec^2x DX ` THEREFORE `int sqrt(tanx)/(sinx cosx)` =`int dt/sqrtt = 2sqrtt +C = 2sqrt(tanx) +c` |
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| 3250. |
Let (d)/(dx) f(x) = (e^(sin x))/(x) , x gt 0. If int_(1)^(4) 3/x e^(sin(x^(3)))dx=F(k)-F(1) then one of the possible value of k is |
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Answer» 63 |
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